Finite Group DatabasebetaFinite Group DatabasebetaOrder 17728.
270 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 111 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #22579878 | C2 | semidirect |
| 3. #22579869 | C2 | semidirect |
| 4. #22579863 | C2 | semidirect |
| 5. #22579856 | C2 | semidirect |
| 6. #22579839 | C2 | semidirect |
| 7. C22×Q8×C277 | C2 | semidirect |
| 52. C277 | #536 | semidirect |
| 55. C22×Q8 | D277 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984563 | 2 |
| #22579878 | 2 |
| #22579869 | 2 |
| #22579863 | 2 |
| #22579856 | 2 |
| #22579839 | 2 |
| C22×Q8×C277 | 2 |
| #536 | 277 |